|InterJournal Complex Systems, 913
|Manuscript Number: |
Submission Date: 2004
|The Evolution of Controllability in Enzyme System Dynamics|
A building block of all living organisms' metabolism is the "enzyme chain." A chemical "substrate" diffuses into the (open) system. A first enzyme transforms it into a first intermediate metabolite. A second enzyme transforms the first intermediate into a second intermediate metabolite. Eventually, an Nth intermediate, the "product" diffuses out of the open system. What we most often see in nature is that the behavior of the first enzyme is regulated by a feedback loop sensitive to the concentration of product. This is accomplished by the first enzyme in the chain being "allosteric", with one active site for binding with the substrate, and a second active site for binding with the product. Normally, as the concentration of product increases, the catalytic efficiency of the first enzyme is decreased (inhibited). To anthropomorphize, when the enzyme chain is making too much product for the organism’s good, the first enzyme in the chain is told: "whoa, slow down there." Such feedback can lead to oscillation, or, as this author first pointed out, "nonperiodic oscillation" (for which, at the time, the term "chaos" had not yet been introduced). But why that single feedback loop, known as "endproduct inhibition" [Umbarger, 1956], and not other possible control systems? What exactly is evolution doing, in adapting systems to do complex things with control of flux (flux meaning the mass of chemicals flowing through the open system in unit time)? This publication emphasizes the results of Kacser and the results of Savageau, in the context of this author’s theory. Other publications by this author [Post, 9 refs] explain the context and literature on the dynamic behavior of enzyme system kinetics in living metabolisms; the use of interactive computer simulations to analyze such behavior; the emergent behaviors "at the edge of chaos"; the mathematical solution in the neighborhood of steady state of previously unsolved systems of nonlinear Michaelis-Menton equations [Michaelis-Menten, 1913]; and a deep reason for those solutions in terms of Krohn-Rhodes Decomposition of the Semigroup of Differential Operators of the systems of nonlinear Michaelis-Menton equations. Living organisms are not test tubes in which are chemical reactions have reached equilibrium. They are made of cells, each cell of which is an "open system" in which energy, entropy, and certain molecules can pass through cell membranes. Due to conservation of mass, the rate of stuff going in (averaged over time) equals the rate of stuff going out. That rate is called "flux." If what comes into the open system varies as a function of time, what is inside the system varies as a function of time, and what leaves the system varies as a function of time. Post's related publications provide a general solution to the relationship between the input function of time and the output function of time, in the neighborhood of steady state. But the behavior of the open system, in its complexity, can also be analyzed in terms of mathematical Control Theory. This leads immediately to questions of "Control of Flux."
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